LMFDB - Embedded newform 1587.2.a.t.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1587,2,Mod(1,1587)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1587, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1587.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1587 = 3 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1587.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$12.6722588008$
Analytic rank:	$1$
Dimension:	$10$
Coefficient field:	10.10.5791333887977.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 2x^{9} - 12x^{8} + 22x^{7} + 49x^{6} - 84x^{5} - 73x^{4} + 132x^{3} + 17x^{2} - 74x + 23 $ x^10 - 2x^9 - 12x^8 + 22x^7 + 49x^6 - 84x^5 - 73x^4 + 132x^3 + 17x^2 - 74*x + 23
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 69)
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Root			$-2.10158$ of defining polynomial
Character	$\chi$	$=$	1587.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.10158 q^{2} +1.00000 q^{3} +2.41664 q^{4} -3.44976 q^{5} +2.10158 q^{6} -1.58175 q^{7} +0.875613 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+2.10158 q^{2} +1.00000 q^{3} +2.41664 q^{4} -3.44976 q^{5} +2.10158 q^{6} -1.58175 q^{7} +0.875613 q^{8} +1.00000 q^{9} -7.24995 q^{10} -1.37979 q^{11} +2.41664 q^{12} -4.55358 q^{13} -3.32418 q^{14} -3.44976 q^{15} -2.99312 q^{16} +4.04550 q^{17} +2.10158 q^{18} -6.10747 q^{19} -8.33685 q^{20} -1.58175 q^{21} -2.89974 q^{22} +0.875613 q^{24} +6.90085 q^{25} -9.56973 q^{26} +1.00000 q^{27} -3.82253 q^{28} -10.0916 q^{29} -7.24995 q^{30} +1.13727 q^{31} -8.04151 q^{32} -1.37979 q^{33} +8.50196 q^{34} +5.45667 q^{35} +2.41664 q^{36} +8.26429 q^{37} -12.8353 q^{38} -4.55358 q^{39} -3.02065 q^{40} +4.90225 q^{41} -3.32418 q^{42} +2.87439 q^{43} -3.33446 q^{44} -3.44976 q^{45} +4.66656 q^{47} -2.99312 q^{48} -4.49806 q^{49} +14.5027 q^{50} +4.04550 q^{51} -11.0044 q^{52} -6.53652 q^{53} +2.10158 q^{54} +4.75994 q^{55} -1.38500 q^{56} -6.10747 q^{57} -21.2084 q^{58} +0.947273 q^{59} -8.33685 q^{60} -0.762386 q^{61} +2.39007 q^{62} -1.58175 q^{63} -10.9136 q^{64} +15.7088 q^{65} -2.89974 q^{66} +2.79290 q^{67} +9.77655 q^{68} +11.4676 q^{70} -5.67469 q^{71} +0.875613 q^{72} +0.910042 q^{73} +17.3681 q^{74} +6.90085 q^{75} -14.7596 q^{76} +2.18249 q^{77} -9.56973 q^{78} -9.74717 q^{79} +10.3255 q^{80} +1.00000 q^{81} +10.3025 q^{82} +4.85439 q^{83} -3.82253 q^{84} -13.9560 q^{85} +6.04077 q^{86} -10.0916 q^{87} -1.20816 q^{88} +3.66643 q^{89} -7.24995 q^{90} +7.20264 q^{91} +1.13727 q^{93} +9.80716 q^{94} +21.0693 q^{95} -8.04151 q^{96} +1.70609 q^{97} -9.45304 q^{98} -1.37979 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 2 q^{2} + 10 q^{3} + 8 q^{4} - 8 q^{5} - 2 q^{6} - 19 q^{7} - 6 q^{8} + 10 q^{9}+O(q^{10}) $ 10 * q - 2 * q^2 + 10 * q^3 + 8 * q^4 - 8 * q^5 - 2 * q^6 - 19 * q^7 - 6 * q^8 + 10 * q^9	\( 10 q - 2 q^{2} + 10 q^{3} + 8 q^{4} - 8 q^{5} - 2 q^{6} - 19 q^{7} - 6 q^{8} + 10 q^{9} - 13 q^{10} - 3 q^{11} + 8 q^{12} - 4 q^{13} - 8 q^{15} - 4 q^{16} - 11 q^{17} - 2 q^{18} - 22 q^{19} - q^{20} - 19 q^{21} - 13 q^{22} - 6 q^{24} - 2 q^{25} + 4 q^{26} + 10 q^{27} - 26 q^{28} - 5 q^{29} - 13 q^{30} - 7 q^{31} - 34 q^{32} - 3 q^{33} - 4 q^{34} + 9 q^{35} + 8 q^{36} - 35 q^{37} + 9 q^{38} - 4 q^{39} - 21 q^{40} - 28 q^{43} + 7 q^{44} - 8 q^{45} + 9 q^{47} - 4 q^{48} + 17 q^{49} - 11 q^{51} - 52 q^{52} - 34 q^{53} - 2 q^{54} - 14 q^{55} + 30 q^{56} - 22 q^{57} - 24 q^{58} - 2 q^{59} - q^{60} - 49 q^{61} - 28 q^{62} - 19 q^{63} + 10 q^{64} - 2 q^{65} - 13 q^{66} - 26 q^{67} + 6 q^{68} + 16 q^{70} + 15 q^{71} - 6 q^{72} + 14 q^{73} + 25 q^{74} - 2 q^{75} - 19 q^{76} - 33 q^{77} + 4 q^{78} - 43 q^{79} + 49 q^{80} + 10 q^{81} + 24 q^{82} + 15 q^{83} - 26 q^{84} - 21 q^{85} + 49 q^{86} - 5 q^{87} - 15 q^{88} + 15 q^{89} - 13 q^{90} - 4 q^{91} - 7 q^{93} - 28 q^{94} + 28 q^{95} - 34 q^{96} - 22 q^{97} + 15 q^{98} - 3 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 + 10 * q^3 + 8 * q^4 - 8 * q^5 - 2 * q^6 - 19 * q^7 - 6 * q^8 + 10 * q^9 - 13 * q^10 - 3 * q^11 + 8 * q^12 - 4 * q^13 - 8 * q^15 - 4 * q^16 - 11 * q^17 - 2 * q^18 - 22 * q^19 - q^20 - 19 * q^21 - 13 * q^22 - 6 * q^24 - 2 * q^25 + 4 * q^26 + 10 * q^27 - 26 * q^28 - 5 * q^29 - 13 * q^30 - 7 * q^31 - 34 * q^32 - 3 * q^33 - 4 * q^34 + 9 * q^35 + 8 * q^36 - 35 * q^37 + 9 * q^38 - 4 * q^39 - 21 * q^40 - 28 * q^43 + 7 * q^44 - 8 * q^45 + 9 * q^47 - 4 * q^48 + 17 * q^49 - 11 * q^51 - 52 * q^52 - 34 * q^53 - 2 * q^54 - 14 * q^55 + 30 * q^56 - 22 * q^57 - 24 * q^58 - 2 * q^59 - q^60 - 49 * q^61 - 28 * q^62 - 19 * q^63 + 10 * q^64 - 2 * q^65 - 13 * q^66 - 26 * q^67 + 6 * q^68 + 16 * q^70 + 15 * q^71 - 6 * q^72 + 14 * q^73 + 25 * q^74 - 2 * q^75 - 19 * q^76 - 33 * q^77 + 4 * q^78 - 43 * q^79 + 49 * q^80 + 10 * q^81 + 24 * q^82 + 15 * q^83 - 26 * q^84 - 21 * q^85 + 49 * q^86 - 5 * q^87 - 15 * q^88 + 15 * q^89 - 13 * q^90 - 4 * q^91 - 7 * q^93 - 28 * q^94 + 28 * q^95 - 34 * q^96 - 22 * q^97 + 15 * q^98 - 3 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.10158	1.48604	0.743021	−	0.669268i	$-0.233392\pi$
$2$	2.10158	1.48604	0.743021	+	0.669268i	$0.233392\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.41664	1.20832
$5$	−3.44976	−1.54278	−0.771390	−	0.636363i	$-0.780438\pi$
$5$	−3.44976	−1.54278	−0.771390	+	0.636363i	$0.780438\pi$
$6$	2.10158	0.857967
$7$	−1.58175	−0.597846	−0.298923	−	0.954277i	$-0.596627\pi$
$7$	−1.58175	−0.597846	−0.298923	+	0.954277i	$0.596627\pi$
$8$	0.875613	0.309576
$9$	1.00000	0.333333
$10$	−7.24995	−2.29264
$11$	−1.37979	−0.416022	−0.208011	−	0.978126i	$-0.566699\pi$
$11$	−1.37979	−0.416022	−0.208011	+	0.978126i	$0.566699\pi$
$12$	2.41664	0.697625
$13$	−4.55358	−1.26294	−0.631468	−	0.775402i	$-0.717547\pi$
$13$	−4.55358	−1.26294	−0.631468	+	0.775402i	$0.717547\pi$
$14$	−3.32418	−0.888425
$15$	−3.44976	−0.890724
$16$	−2.99312	−0.748279
$17$	4.04550	0.981179	0.490589	−	0.871391i	$-0.336782\pi$
$17$	4.04550	0.981179	0.490589	+	0.871391i	$0.336782\pi$
$18$	2.10158	0.495348
$19$	−6.10747	−1.40115	−0.700574	−	0.713579i	$-0.747073\pi$
$19$	−6.10747	−1.40115	−0.700574	+	0.713579i	$0.747073\pi$
$20$	−8.33685	−1.86418
$21$	−1.58175	−0.345167
$22$	−2.89974	−0.618227
$23$	0	0
$23$	0	0
$24$	0.875613	0.178734
$25$	6.90085	1.38017
$26$	−9.56973	−1.87678
$27$	1.00000	0.192450
$28$	−3.82253	−0.722391
$29$	−10.0916	−1.87397	−0.936983	−	0.349374i	$-0.886394\pi$
$29$	−10.0916	−1.87397	−0.936983	+	0.349374i	$0.886394\pi$
$30$	−7.24995	−1.32365
$31$	1.13727	0.204260	0.102130	−	0.994771i	$-0.467434\pi$
$31$	1.13727	0.204260	0.102130	+	0.994771i	$0.467434\pi$
$32$	−8.04151	−1.42155
$33$	−1.37979	−0.240190
$34$	8.50196	1.45807
$35$	5.45667	0.922345
$36$	2.41664	0.402774
$37$	8.26429	1.35864	0.679320	−	0.733842i	$-0.262275\pi$
$37$	8.26429	1.35864	0.679320	+	0.733842i	$0.262275\pi$
$38$	−12.8353	−2.08217
$39$	−4.55358	−0.729157
$40$	−3.02065	−0.477607
$41$	4.90225	0.765603	0.382802	−	0.923831i	$-0.374959\pi$
$41$	4.90225	0.765603	0.382802	+	0.923831i	$0.374959\pi$
$42$	−3.32418	−0.512932
$43$	2.87439	0.438340	0.219170	−	0.975687i	$-0.429665\pi$
$43$	2.87439	0.438340	0.219170	+	0.975687i	$0.429665\pi$
$44$	−3.33446	−0.502689
$45$	−3.44976	−0.514260
$46$	0	0
$47$	4.66656	0.680688	0.340344	−	0.940301i	$-0.389456\pi$
$47$	4.66656	0.680688	0.340344	+	0.940301i	$0.389456\pi$
$48$	−2.99312	−0.432019
$49$	−4.49806	−0.642580
$50$	14.5027	2.05099
$51$	4.04550	0.566484
$52$	−11.0044	−1.52603
$53$	−6.53652	−0.897859	−0.448930	−	0.893567i	$-0.648195\pi$
$53$	−6.53652	−0.897859	−0.448930	+	0.893567i	$0.648195\pi$
$54$	2.10158	0.285989
$55$	4.75994	0.641831
$56$	−1.38500	−0.185079
$57$	−6.10747	−0.808954
$58$	−21.2084	−2.78479
$59$	0.947273	0.123324	0.0616622	−	0.998097i	$-0.480360\pi$
$59$	0.947273	0.123324	0.0616622	+	0.998097i	$0.480360\pi$
$60$	−8.33685	−1.07628
$61$	−0.762386	−0.0976135	−0.0488068	−	0.998808i	$-0.515542\pi$
$61$	−0.762386	−0.0976135	−0.0488068	+	0.998808i	$0.515542\pi$
$62$	2.39007	0.303539
$63$	−1.58175	−0.199282
$64$	−10.9136	−1.36421
$65$	15.7088	1.94843
$66$	−2.89974	−0.356933
$67$	2.79290	0.341207	0.170603	−	0.985340i	$-0.445428\pi$
$67$	2.79290	0.341207	0.170603	+	0.985340i	$0.445428\pi$
$68$	9.77655	1.18558
$69$	0	0
$70$	11.4676	1.37064
$71$	−5.67469	−0.673462	−0.336731	−	0.941601i	$-0.609321\pi$
$71$	−5.67469	−0.673462	−0.336731	+	0.941601i	$0.609321\pi$
$72$	0.875613	0.103192
$73$	0.910042	0.106512	0.0532562	−	0.998581i	$-0.483040\pi$
$73$	0.910042	0.106512	0.0532562	+	0.998581i	$0.483040\pi$
$74$	17.3681	2.01900
$75$	6.90085	0.796842
$76$	−14.7596	−1.69304
$77$	2.18249	0.248717
$78$	−9.56973	−1.08356
$79$	−9.74717	−1.09664	−0.548321	−	0.836268i	$-0.684733\pi$
$79$	−9.74717	−1.09664	−0.548321	+	0.836268i	$0.684733\pi$
$80$	10.3255	1.15443
$81$	1.00000	0.111111
$82$	10.3025	1.13772
$83$	4.85439	0.532838	0.266419	−	0.963857i	$-0.414159\pi$
$83$	4.85439	0.532838	0.266419	+	0.963857i	$0.414159\pi$
$84$	−3.82253	−0.417073
$85$	−13.9560	−1.51374
$86$	6.04077	0.651392
$87$	−10.0916	−1.08194
$88$	−1.20816	−0.128790
$89$	3.66643	0.388641	0.194321	−	0.980938i	$-0.437750\pi$
$89$	3.66643	0.388641	0.194321	+	0.980938i	$0.437750\pi$
$90$	−7.24995	−0.764212
$91$	7.20264	0.755042
$92$	0	0
$93$	1.13727	0.117929
$94$	9.80716	1.01153
$95$	21.0693	2.16166
$96$	−8.04151	−0.820733
$97$	1.70609	0.173227	0.0866137	−	0.996242i	$-0.472395\pi$
$97$	1.70609	0.173227	0.0866137	+	0.996242i	$0.472395\pi$
$98$	−9.45304	−0.954901
$99$	−1.37979	−0.138674
$100$	16.6769	1.66769
$101$	6.88534	0.685117	0.342558	−	0.939497i	$-0.388707\pi$
$101$	6.88534	0.685117	0.342558	+	0.939497i	$0.388707\pi$
$102$	8.50196	0.841819
$103$	−0.287590	−0.0283371	−0.0141685	−	0.999900i	$-0.504510\pi$
$103$	−0.287590	−0.0283371	−0.0141685	+	0.999900i	$0.504510\pi$
$104$	−3.98717	−0.390975
$105$	5.45667	0.532516
$106$	−13.7370	−1.33426
$107$	−8.29060	−0.801483	−0.400741	−	0.916191i	$-0.631247\pi$
$107$	−8.29060	−0.801483	−0.400741	+	0.916191i	$0.631247\pi$
$108$	2.41664	0.232542
$109$	−20.5483	−1.96817	−0.984085	−	0.177697i	$-0.943135\pi$
$109$	−20.5483	−1.96817	−0.984085	+	0.177697i	$0.943135\pi$
$110$	10.0034	0.953788
$111$	8.26429	0.784411
$112$	4.73437	0.447356
$113$	1.62281	0.152661	0.0763307	−	0.997083i	$-0.475680\pi$
$113$	1.62281	0.152661	0.0763307	+	0.997083i	$0.475680\pi$
$114$	−12.8353	−1.20214
$115$	0	0
$116$	−24.3879	−2.26436
$117$	−4.55358	−0.420979
$118$	1.99077	0.183265
$119$	−6.39899	−0.586594
$120$	−3.02065	−0.275747
$121$	−9.09618	−0.826926
$122$	−1.60222	−0.145058
$123$	4.90225	0.442021
$124$	2.74838	0.246812
$125$	−6.55748	−0.586519
$126$	−3.32418	−0.296142
$127$	9.69077	0.859917	0.429958	−	0.902849i	$-0.358528\pi$
$127$	9.69077	0.859917	0.429958	+	0.902849i	$0.358528\pi$
$128$	−6.85290	−0.605717
$129$	2.87439	0.253076
$130$	33.0133	2.89545
$131$	11.4566	1.00097	0.500486	−	0.865745i	$-0.333155\pi$
$131$	11.4566	1.00097	0.500486	+	0.865745i	$0.333155\pi$
$132$	−3.33446	−0.290228
$133$	9.66050	0.837672
$134$	5.86950	0.507047
$135$	−3.44976	−0.296908
$136$	3.54229	0.303749
$137$	−1.64372	−0.140433	−0.0702163	−	0.997532i	$-0.522369\pi$
$137$	−1.64372	−0.140433	−0.0702163	+	0.997532i	$0.522369\pi$
$138$	0	0
$139$	−5.57603	−0.472952	−0.236476	−	0.971637i	$-0.575993\pi$
$139$	−5.57603	−0.472952	−0.236476	+	0.971637i	$0.575993\pi$
$140$	13.1868	1.11449
$141$	4.66656	0.392995
$142$	−11.9258	−1.00079
$143$	6.28298	0.525410
$144$	−2.99312	−0.249426
$145$	34.8137	2.89112
$146$	1.91253	0.158282
$147$	−4.49806	−0.370994
$148$	19.9718	1.64168
$149$	−6.08189	−0.498248	−0.249124	−	0.968472i	$-0.580143\pi$
$149$	−6.08189	−0.498248	−0.249124	+	0.968472i	$0.580143\pi$
$150$	14.5027	1.18414
$151$	−23.6673	−1.92601	−0.963007	−	0.269476i	$-0.913149\pi$
$151$	−23.6673	−1.92601	−0.963007	+	0.269476i	$0.913149\pi$
$152$	−5.34777	−0.433762
$153$	4.04550	0.327060
$154$	4.58667	0.369604
$155$	−3.92331	−0.315128
$156$	−11.0044	−0.881056
$157$	−15.5790	−1.24334	−0.621672	−	0.783278i	$-0.713546\pi$
$157$	−15.5790	−1.24334	−0.621672	+	0.783278i	$0.713546\pi$
$158$	−20.4845	−1.62966
$159$	−6.53652	−0.518379
$160$	27.7413	2.19314
$161$	0	0
$162$	2.10158	0.165116
$163$	−6.16185	−0.482633	−0.241317	−	0.970446i	$-0.577579\pi$
$163$	−6.16185	−0.482633	−0.241317	+	0.970446i	$0.577579\pi$
$164$	11.8470	0.925096
$165$	4.75994	0.370561
$166$	10.2019	0.791820
$167$	9.44372	0.730777	0.365388	−	0.930855i	$-0.380936\pi$
$167$	9.44372	0.730777	0.365388	+	0.930855i	$0.380936\pi$
$168$	−1.38500	−0.106855
$169$	7.73512	0.595009
$170$	−29.3297	−2.24949
$171$	−6.10747	−0.467050
$172$	6.94638	0.529656
$173$	7.09393	0.539341	0.269671	−	0.962953i	$-0.413085\pi$
$173$	7.09393	0.539341	0.269671	+	0.962953i	$0.413085\pi$
$174$	−21.2084	−1.60780
$175$	−10.9154	−0.825130
$176$	4.12987	0.311301
$177$	0.947273	0.0712014
$178$	7.70531	0.577537
$179$	8.02689	0.599958	0.299979	−	0.953946i	$-0.403020\pi$
$179$	8.02689	0.599958	0.299979	+	0.953946i	$0.403020\pi$
$180$	−8.33685	−0.621392
$181$	11.7891	0.876274	0.438137	−	0.898908i	$-0.355638\pi$
$181$	11.7891	0.876274	0.438137	+	0.898908i	$0.355638\pi$
$182$	15.1369	1.12202
$183$	−0.762386	−0.0563572
$184$	0	0
$185$	−28.5098	−2.09608
$186$	2.39007	0.175248
$187$	−5.58194	−0.408192
$188$	11.2774	0.822491
$189$	−1.58175	−0.115056
$190$	44.2788	3.21233
$191$	26.4497	1.91384	0.956918	−	0.290358i	$-0.0937745\pi$
$191$	26.4497	1.91384	0.956918	+	0.290358i	$0.0937745\pi$
$192$	−10.9136	−0.787624
$193$	18.8490	1.35678	0.678389	−	0.734703i	$-0.262679\pi$
$193$	18.8490	1.35678	0.678389	+	0.734703i	$0.262679\pi$
$194$	3.58549	0.257423
$195$	15.7088	1.12493
$196$	−10.8702	−0.776443
$197$	8.81816	0.628268	0.314134	−	0.949379i	$-0.398286\pi$
$197$	8.81816	0.628268	0.314134	+	0.949379i	$0.398286\pi$
$198$	−2.89974	−0.206076
$199$	−15.0061	−1.06375	−0.531876	−	0.846822i	$-0.678513\pi$
$199$	−15.0061	−1.06375	−0.531876	+	0.846822i	$0.678513\pi$
$200$	6.04247	0.427267
$201$	2.79290	0.196996
$202$	14.4701	1.01811
$203$	15.9624	1.12034
$204$	9.77655	0.684495
$205$	−16.9116	−1.18116
$206$	−0.604394	−0.0421101
$207$	0	0
$208$	13.6294	0.945030
$209$	8.42702	0.582909
$210$	11.4676	0.791342
$211$	−26.7256	−1.83987	−0.919933	−	0.392075i	$-0.871757\pi$
$211$	−26.7256	−1.83987	−0.919933	+	0.392075i	$0.871757\pi$
$212$	−15.7964	−1.08490
$213$	−5.67469	−0.388824
$214$	−17.4234	−1.19104
$215$	−9.91596	−0.676263
$216$	0.875613	0.0595779
$217$	−1.79888	−0.122116
$218$	−43.1839	−2.92479
$219$	0.910042	0.0614950
$220$	11.5031	0.775538
$221$	−18.4215	−1.23917
$222$	17.3681	1.16567
$223$	12.2946	0.823310	0.411655	−	0.911340i	$-0.364951\pi$
$223$	12.2946	0.823310	0.411655	+	0.911340i	$0.364951\pi$
$224$	12.7197	0.849869
$225$	6.90085	0.460057
$226$	3.41047	0.226861
$227$	16.4827	1.09400	0.546998	−	0.837134i	$-0.315771\pi$
$227$	16.4827	1.09400	0.546998	+	0.837134i	$0.315771\pi$
$228$	−14.7596	−0.977477
$229$	0.636413	0.0420554	0.0210277	−	0.999779i	$-0.493306\pi$
$229$	0.636413	0.0420554	0.0210277	+	0.999779i	$0.493306\pi$
$230$	0	0
$231$	2.18249	0.143597
$232$	−8.83635	−0.580135
$233$	0.643582	0.0421625	0.0210812	−	0.999778i	$-0.493289\pi$
$233$	0.643582	0.0421625	0.0210812	+	0.999778i	$0.493289\pi$
$234$	−9.56973	−0.625593
$235$	−16.0985	−1.05015
$236$	2.28922	0.149016
$237$	−9.74717	−0.633147
$238$	−13.4480	−0.871704
$239$	−9.62895	−0.622845	−0.311422	−	0.950272i	$-0.600805\pi$
$239$	−9.62895	−0.622845	−0.311422	+	0.950272i	$0.600805\pi$
$240$	10.3255	0.666511
$241$	5.96496	0.384237	0.192119	−	0.981372i	$-0.438464\pi$
$241$	5.96496	0.384237	0.192119	+	0.981372i	$0.438464\pi$
$242$	−19.1164	−1.22885
$243$	1.00000	0.0641500
$244$	−1.84242	−0.117949
$245$	15.5172	0.991359
$246$	10.3025	0.656862
$247$	27.8109	1.76956
$248$	0.995808	0.0632339
$249$	4.85439	0.307634
$250$	−13.7811	−0.871592
$251$	3.85471	0.243307	0.121654	−	0.992573i	$-0.461180\pi$
$251$	3.85471	0.243307	0.121654	+	0.992573i	$0.461180\pi$
$252$	−3.82253	−0.240797
$253$	0	0
$254$	20.3659	1.27787
$255$	−13.9560	−0.873960
$256$	7.42536	0.464085
$257$	−11.8109	−0.736741	−0.368371	−	0.929679i	$-0.620084\pi$
$257$	−11.8109	−0.736741	−0.368371	+	0.929679i	$0.620084\pi$
$258$	6.04077	0.376082
$259$	−13.0721	−0.812258
$260$	37.9625	2.35434
$261$	−10.0916	−0.624656
$262$	24.0771	1.48749
$263$	−14.6534	−0.903569	−0.451784	−	0.892127i	$-0.649212\pi$
$263$	−14.6534	−0.903569	−0.451784	+	0.892127i	$0.649212\pi$
$264$	−1.20816	−0.0743572
$265$	22.5494	1.38520
$266$	20.3023	1.24482
$267$	3.66643	0.224382
$268$	6.74944	0.412288
$269$	−27.2170	−1.65945	−0.829724	−	0.558174i	$-0.811502\pi$
$269$	−27.2170	−1.65945	−0.829724	+	0.558174i	$0.811502\pi$
$270$	−7.24995	−0.441218
$271$	−4.28396	−0.260232	−0.130116	−	0.991499i	$-0.541535\pi$
$271$	−4.28396	−0.260232	−0.130116	+	0.991499i	$0.541535\pi$
$272$	−12.1087	−0.734196
$273$	7.20264	0.435924
$274$	−3.45442	−0.208689
$275$	−9.52172	−0.574181
$276$	0	0
$277$	6.86176	0.412283	0.206142	−	0.978522i	$-0.433909\pi$
$277$	6.86176	0.412283	0.206142	+	0.978522i	$0.433909\pi$
$278$	−11.7185	−0.702827
$279$	1.13727	0.0680866
$280$	4.77793	0.285536
$281$	13.3058	0.793755	0.396878	−	0.917871i	$-0.370094\pi$
$281$	13.3058	0.793755	0.396878	+	0.917871i	$0.370094\pi$
$282$	9.80716	0.584008
$283$	−19.2217	−1.14261	−0.571307	−	0.820736i	$-0.693563\pi$
$283$	−19.2217	−1.14261	−0.571307	+	0.820736i	$0.693563\pi$
$284$	−13.7137	−0.813759
$285$	21.0693	1.24804
$286$	13.2042	0.780781
$287$	−7.75415	−0.457713
$288$	−8.04151	−0.473850
$289$	−0.633899	−0.0372882
$290$	73.1638	4.29633
$291$	1.70609	0.100013
$292$	2.19925	0.128701
$293$	−13.6447	−0.797133	−0.398566	−	0.917139i	$-0.630492\pi$
$293$	−13.6447	−0.797133	−0.398566	+	0.917139i	$0.630492\pi$
$294$	−9.45304	−0.551312
$295$	−3.26786	−0.190262
$296$	7.23631	0.420602
$297$	−1.37979	−0.0800635
$298$	−12.7816	−0.740417
$299$	0	0
$300$	16.6769	0.962842
$301$	−4.54657	−0.262060
$302$	−49.7387	−2.86214
$303$	6.88534	0.395552
$304$	18.2804	1.04845
$305$	2.63005	0.150596
$306$	8.50196	0.486024
$307$	−25.4313	−1.45144	−0.725721	−	0.687989i	$-0.758494\pi$
$307$	−25.4313	−1.45144	−0.725721	+	0.687989i	$0.758494\pi$
$308$	5.27429	0.300531
$309$	−0.287590	−0.0163604
$310$	−8.24516	−0.468294
$311$	−31.4782	−1.78496	−0.892481	−	0.451085i	$-0.851037\pi$
$311$	−31.4782	−1.78496	−0.892481	+	0.451085i	$0.851037\pi$
$312$	−3.98717	−0.225729
$313$	−13.4694	−0.761338	−0.380669	−	0.924711i	$-0.624306\pi$
$313$	−13.4694	−0.761338	−0.380669	+	0.924711i	$0.624306\pi$
$314$	−32.7406	−1.84766
$315$	5.45667	0.307448
$316$	−23.5554	−1.32510
$317$	−3.84870	−0.216165	−0.108082	−	0.994142i	$-0.534471\pi$
$317$	−3.84870	−0.216165	−0.108082	+	0.994142i	$0.534471\pi$
$318$	−13.7370	−0.770334
$319$	13.9243	0.779612
$320$	37.6495	2.10467
$321$	−8.29060	−0.462736
$322$	0	0
$323$	−24.7078	−1.37478
$324$	2.41664	0.134258
$325$	−31.4236	−1.74307
$326$	−12.9496	−0.717214
$327$	−20.5483	−1.13632
$328$	4.29247	0.237012
$329$	−7.38135	−0.406947
$330$	10.0034	0.550669
$331$	−20.2085	−1.11076	−0.555381	−	0.831596i	$-0.687427\pi$
$331$	−20.2085	−1.11076	−0.555381	+	0.831596i	$0.687427\pi$
$332$	11.7313	0.643840
$333$	8.26429	0.452880
$334$	19.8467	1.08597
$335$	−9.63482	−0.526407
$336$	4.73437	0.258281
$337$	−11.0123	−0.599877	−0.299939	−	0.953959i	$-0.596966\pi$
$337$	−11.0123	−0.599877	−0.299939	+	0.953959i	$0.596966\pi$
$338$	16.2560	0.884209
$339$	1.62281	0.0881391
$340$	−33.7267	−1.82909
$341$	−1.56919	−0.0849766
$342$	−12.8353	−0.694056
$343$	18.1871	0.982010
$344$	2.51685	0.135700
$345$	0	0
$346$	14.9085	0.801484
$347$	−26.3629	−1.41523	−0.707617	−	0.706596i	$-0.750230\pi$
$347$	−26.3629	−1.41523	−0.707617	+	0.706596i	$0.750230\pi$
$348$	−24.3879	−1.30733
$349$	18.6963	1.00079	0.500394	−	0.865798i	$-0.333188\pi$
$349$	18.6963	1.00079	0.500394	+	0.865798i	$0.333188\pi$
$350$	−22.9397	−1.22618
$351$	−4.55358	−0.243052
$352$	11.0956	0.591397
$353$	23.5876	1.25544	0.627722	−	0.778438i	$-0.283988\pi$
$353$	23.5876	1.25544	0.627722	+	0.778438i	$0.283988\pi$
$354$	1.99077	0.105808
$355$	19.5763	1.03900
$356$	8.86047	0.469604
$357$	−6.39899	−0.338670
$358$	16.8692	0.891563
$359$	15.0554	0.794594	0.397297	−	0.917690i	$-0.369948\pi$
$359$	15.0554	0.794594	0.397297	+	0.917690i	$0.369948\pi$
$360$	−3.02065	−0.159202
$361$	18.3011	0.963218
$362$	24.7757	1.30218
$363$	−9.09618	−0.477426
$364$	17.4062	0.912334
$365$	−3.13943	−0.164325
$366$	−1.60222	−0.0837492
$367$	−33.1504	−1.73043	−0.865217	−	0.501397i	$-0.832820\pi$
$367$	−33.1504	−1.73043	−0.865217	+	0.501397i	$0.832820\pi$
$368$	0	0
$369$	4.90225	0.255201
$370$	−59.9157	−3.11487
$371$	10.3392	0.536782
$372$	2.74838	0.142497
$373$	−32.9380	−1.70546	−0.852732	−	0.522349i	$-0.825056\pi$
$373$	−32.9380	−1.70546	−0.852732	+	0.522349i	$0.825056\pi$
$374$	−11.7309	−0.606591
$375$	−6.55748	−0.338627
$376$	4.08610	0.210725
$377$	45.9530	2.36670
$378$	−3.32418	−0.170977
$379$	−22.0053	−1.13034	−0.565168	−	0.824976i	$-0.691189\pi$
$379$	−22.0053	−1.13034	−0.565168	+	0.824976i	$0.691189\pi$
$380$	50.9170	2.61199
$381$	9.69077	0.496473
$382$	55.5863	2.84404
$383$	−4.68252	−0.239266	−0.119633	−	0.992818i	$-0.538172\pi$
$383$	−4.68252	−0.239266	−0.119633	+	0.992818i	$0.538172\pi$
$384$	−6.85290	−0.349711
$385$	−7.52905	−0.383716
$386$	39.6126	2.01623
$387$	2.87439	0.146113
$388$	4.12302	0.209315
$389$	14.0305	0.711373	0.355687	−	0.934605i	$-0.384247\pi$
$389$	14.0305	0.711373	0.355687	+	0.934605i	$0.384247\pi$
$390$	33.0133	1.67169
$391$	0	0
$392$	−3.93856	−0.198927
$393$	11.4566	0.577911
$394$	18.5321	0.933633
$395$	33.6254	1.69188
$396$	−3.33446	−0.167563
$397$	11.2613	0.565189	0.282595	−	0.959239i	$-0.408805\pi$
$397$	11.2613	0.565189	0.282595	+	0.959239i	$0.408805\pi$
$398$	−31.5365	−1.58078
$399$	9.66050	0.483630
$400$	−20.6551	−1.03275
$401$	17.1233	0.855097	0.427548	−	0.903992i	$-0.359377\pi$
$401$	17.1233	0.855097	0.427548	+	0.903992i	$0.359377\pi$
$402$	5.86950	0.292744
$403$	−5.17866	−0.257967
$404$	16.6394	0.827842
$405$	−3.44976	−0.171420
$406$	33.5464	1.66488
$407$	−11.4030	−0.565224
$408$	3.54229	0.175370
$409$	−8.98166	−0.444115	−0.222057	−	0.975034i	$-0.571277\pi$
$409$	−8.98166	−0.444115	−0.222057	+	0.975034i	$0.571277\pi$
$410$	−35.5411	−1.75525
$411$	−1.64372	−0.0810788
$412$	−0.695003	−0.0342403
$413$	−1.49835	−0.0737290
$414$	0	0
$415$	−16.7465	−0.822052
$416$	36.6177	1.79533
$417$	−5.57603	−0.273059
$418$	17.7101	0.866227
$419$	7.04191	0.344020	0.172010	−	0.985095i	$-0.444974\pi$
$419$	7.04191	0.344020	0.172010	+	0.985095i	$0.444974\pi$
$420$	13.1868	0.643451
$421$	−12.2973	−0.599332	−0.299666	−	0.954044i	$-0.596875\pi$
$421$	−12.2973	−0.599332	−0.299666	+	0.954044i	$0.596875\pi$
$422$	−56.1660	−2.73412
$423$	4.66656	0.226896
$424$	−5.72346	−0.277956
$425$	27.9174	1.35419
$426$	−11.9258	−0.577808
$427$	1.20591	0.0583579
$428$	−20.0354	−0.968450
$429$	6.28298	0.303345
$430$	−20.8392	−1.00496
$431$	−5.04310	−0.242917	−0.121459	−	0.992596i	$-0.538757\pi$
$431$	−5.04310	−0.242917	−0.121459	+	0.992596i	$0.538757\pi$
$432$	−2.99312	−0.144006
$433$	0.889545	0.0427488	0.0213744	−	0.999772i	$-0.493196\pi$
$433$	0.889545	0.0427488	0.0213744	+	0.999772i	$0.493196\pi$
$434$	−3.78049	−0.181470
$435$	34.8137	1.66919
$436$	−49.6580	−2.37818
$437$	0	0
$438$	1.91253	0.0913841
$439$	39.8837	1.90354	0.951772	−	0.306807i	$-0.0992607\pi$
$439$	39.8837	1.90354	0.951772	+	0.306807i	$0.0992607\pi$
$440$	4.16787	0.198695
$441$	−4.49806	−0.214193
$442$	−38.7144	−1.84145
$443$	12.8103	0.608636	0.304318	−	0.952570i	$-0.401571\pi$
$443$	12.8103	0.608636	0.304318	+	0.952570i	$0.401571\pi$
$444$	19.9718	0.947822
$445$	−12.6483	−0.599588
$446$	25.8382	1.22347
$447$	−6.08189	−0.287663
$448$	17.2627	0.815585
$449$	−13.3440	−0.629744	−0.314872	−	0.949134i	$-0.601962\pi$
$449$	−13.3440	−0.629744	−0.314872	+	0.949134i	$0.601962\pi$
$450$	14.5027	0.683664
$451$	−6.76408	−0.318508
$452$	3.92176	0.184464
$453$	−23.6673	−1.11198
$454$	34.6398	1.62572
$455$	−24.8474	−1.16486
$456$	−5.34777	−0.250432
$457$	−23.0625	−1.07882	−0.539409	−	0.842044i	$-0.681352\pi$
$457$	−23.0625	−1.07882	−0.539409	+	0.842044i	$0.681352\pi$
$458$	1.33747	0.0624961
$459$	4.04550	0.188828
$460$	0	0
$461$	−7.59985	−0.353960	−0.176980	−	0.984214i	$-0.556633\pi$
$461$	−7.59985	−0.353960	−0.176980	+	0.984214i	$0.556633\pi$
$462$	4.58667	0.213391
$463$	10.1675	0.472522	0.236261	−	0.971690i	$-0.424078\pi$
$463$	10.1675	0.472522	0.236261	+	0.971690i	$0.424078\pi$
$464$	30.2054	1.40225
$465$	−3.92331	−0.181939
$466$	1.35254	0.0626552
$467$	10.3330	0.478154	0.239077	−	0.971001i	$-0.423155\pi$
$467$	10.3330	0.478154	0.239077	+	0.971001i	$0.423155\pi$
$468$	−11.0044	−0.508678
$469$	−4.41767	−0.203989
$470$	−33.8324	−1.56057
$471$	−15.5790	−0.717844
$472$	0.829444	0.0381783
$473$	−3.96605	−0.182359
$474$	−20.4845	−0.940883
$475$	−42.1467	−1.93382
$476$	−15.4641	−0.708795
$477$	−6.53652	−0.299286
$478$	−20.2360	−0.925574
$479$	8.71133	0.398031	0.199015	−	0.979996i	$-0.436226\pi$
$479$	8.71133	0.398031	0.199015	+	0.979996i	$0.436226\pi$
$480$	27.7413	1.26621
$481$	−37.6321	−1.71588
$482$	12.5359	0.570993
$483$	0	0
$484$	−21.9822	−0.999193
$485$	−5.88561	−0.267252
$486$	2.10158	0.0953297
$487$	22.7674	1.03169	0.515844	−	0.856682i	$-0.327478\pi$
$487$	22.7674	1.03169	0.515844	+	0.856682i	$0.327478\pi$
$488$	−0.667555	−0.0302188
$489$	−6.16185	−0.278649
$490$	32.6107	1.47320
$491$	28.0432	1.26557	0.632785	−	0.774328i	$-0.281912\pi$
$491$	28.0432	1.26557	0.632785	+	0.774328i	$0.281912\pi$
$492$	11.8470	0.534104
$493$	−40.8257	−1.83870
$494$	58.4468	2.62964
$495$	4.75994	0.213944
$496$	−3.40398	−0.152843
$497$	8.97596	0.402627
$498$	10.2019	0.457158
$499$	−14.6488	−0.655771	−0.327885	−	0.944718i	$-0.606336\pi$
$499$	−14.6488	−0.655771	−0.327885	+	0.944718i	$0.606336\pi$
$500$	−15.8471	−0.708704
$501$	9.44372	0.421914
$502$	8.10099	0.361565
$503$	1.61306	0.0719230	0.0359615	−	0.999353i	$-0.488551\pi$
$503$	1.61306	0.0719230	0.0359615	+	0.999353i	$0.488551\pi$
$504$	−1.38500	−0.0616929
$505$	−23.7528	−1.05698
$506$	0	0
$507$	7.73512	0.343529
$508$	23.4191	1.03906
$509$	−24.4829	−1.08518	−0.542592	−	0.839997i	$-0.682557\pi$
$509$	−24.4829	−1.08518	−0.542592	+	0.839997i	$0.682557\pi$
$510$	−29.3297	−1.29874
$511$	−1.43946	−0.0636781
$512$	29.3108	1.29537
$513$	−6.10747	−0.269651
$514$	−24.8215	−1.09483
$515$	0.992117	0.0437179
$516$	6.94638	0.305797
$517$	−6.43887	−0.283181
$518$	−27.4720	−1.20705
$519$	7.09393	0.311389
$520$	13.7548	0.603188
$521$	36.3502	1.59253	0.796265	−	0.604949i	$-0.206806\pi$
$521$	36.3502	1.59253	0.796265	+	0.604949i	$0.206806\pi$
$522$	−21.2084	−0.928265
$523$	18.1125	0.792005	0.396002	−	0.918249i	$-0.370397\pi$
$523$	18.1125	0.792005	0.396002	+	0.918249i	$0.370397\pi$
$524$	27.6866	1.20950
$525$	−10.9154	−0.476389
$526$	−30.7954	−1.34274
$527$	4.60083	0.200415
$528$	4.12987	0.179730
$529$	0	0
$530$	47.3894	2.05847
$531$	0.947273	0.0411081
$532$	23.3460	1.01218
$533$	−22.3228	−0.966908
$534$	7.70531	0.333441
$535$	28.6006	1.23651
$536$	2.44550	0.105629
$537$	8.02689	0.346386
$538$	−57.1987	−2.46601
$539$	6.20637	0.267327
$540$	−8.33685	−0.358761
$541$	36.2904	1.56025	0.780123	−	0.625627i	$-0.215157\pi$
$541$	36.2904	1.56025	0.780123	+	0.625627i	$0.215157\pi$
$542$	−9.00308	−0.386716
$543$	11.7891	0.505917
$544$	−32.5319	−1.39480
$545$	70.8867	3.03645
$546$	15.1369	0.647801
$547$	−11.5431	−0.493548	−0.246774	−	0.969073i	$-0.579371\pi$
$547$	−11.5431	−0.493548	−0.246774	+	0.969073i	$0.579371\pi$
$548$	−3.97229	−0.169688
$549$	−0.762386	−0.0325378
$550$	−20.0107	−0.853258
$551$	61.6342	2.62571
$552$	0	0
$553$	15.4176	0.655623
$554$	14.4205	0.612670
$555$	−28.5098	−1.21017
$556$	−13.4753	−0.571479
$557$	−16.9829	−0.719588	−0.359794	−	0.933032i	$-0.617153\pi$
$557$	−16.9829	−0.719588	−0.359794	+	0.933032i	$0.617153\pi$
$558$	2.39007	0.101180
$559$	−13.0888	−0.553596
$560$	−16.3325	−0.690172
$561$	−5.58194	−0.235670
$562$	27.9632	1.17955
$563$	−16.4137	−0.691753	−0.345877	−	0.938280i	$-0.612418\pi$
$563$	−16.4137	−0.691753	−0.345877	+	0.938280i	$0.612418\pi$
$564$	11.2774	0.474865
$565$	−5.59832	−0.235523
$566$	−40.3961	−1.69797
$567$	−1.58175	−0.0664274
$568$	−4.96883	−0.208488
$569$	0.755568	0.0316751	0.0158375	−	0.999875i	$-0.494959\pi$
$569$	0.755568	0.0316751	0.0158375	+	0.999875i	$0.494959\pi$
$570$	44.2788	1.85464
$571$	−27.0996	−1.13408	−0.567040	−	0.823690i	$-0.691912\pi$
$571$	−27.0996	−1.13408	−0.567040	+	0.823690i	$0.691912\pi$
$572$	15.1837	0.634864
$573$	26.4497	1.10495
$574$	−16.2960	−0.680181
$575$	0	0
$576$	−10.9136	−0.454735
$577$	9.51857	0.396263	0.198132	−	0.980175i	$-0.436513\pi$
$577$	9.51857	0.396263	0.198132	+	0.980175i	$0.436513\pi$
$578$	−1.33219	−0.0554118
$579$	18.8490	0.783336
$580$	84.1323	3.49340
$581$	−7.67844	−0.318555
$582$	3.58549	0.148623
$583$	9.01901	0.373529
$584$	0.796845	0.0329737
$585$	15.7088	0.649478
$586$	−28.6755	−1.18457
$587$	42.7401	1.76407	0.882036	−	0.471182i	$-0.156172\pi$
$587$	42.7401	1.76407	0.882036	+	0.471182i	$0.156172\pi$
$588$	−10.8702	−0.448280
$589$	−6.94584	−0.286198
$590$	−6.86768	−0.282738
$591$	8.81816	0.362731
$592$	−24.7360	−1.01664
$593$	−12.7912	−0.525272	−0.262636	−	0.964895i	$-0.584592\pi$
$593$	−12.7912	−0.525272	−0.262636	+	0.964895i	$0.584592\pi$
$594$	−2.89974	−0.118978
$595$	22.0750	0.904986
$596$	−14.6978	−0.602044
$597$	−15.0061	−0.614158
$598$	0	0
$599$	27.4971	1.12350	0.561751	−	0.827306i	$-0.310128\pi$
$599$	27.4971	1.12350	0.561751	+	0.827306i	$0.310128\pi$
$600$	6.04247	0.246683
$601$	34.1537	1.39316	0.696579	−	0.717480i	$-0.254705\pi$
$601$	34.1537	1.39316	0.696579	+	0.717480i	$0.254705\pi$
$602$	−9.55500	−0.389433
$603$	2.79290	0.113736
$604$	−57.1953	−2.32725
$605$	31.3797	1.27576
$606$	14.4701	0.587807
$607$	−29.9922	−1.21735	−0.608673	−	0.793421i	$-0.708298\pi$
$607$	−29.9922	−1.21735	−0.608673	+	0.793421i	$0.708298\pi$
$608$	49.1132	1.99180
$609$	15.9624	0.646831
$610$	5.52726	0.223792
$611$	−21.2496	−0.859666
$612$	9.77655	0.395193
$613$	−6.66283	−0.269109	−0.134555	−	0.990906i	$-0.542960\pi$
$613$	−6.66283	−0.269109	−0.134555	+	0.990906i	$0.542960\pi$
$614$	−53.4460	−2.15691
$615$	−16.9116	−0.681942
$616$	1.91101	0.0769969
$617$	−28.5932	−1.15112	−0.575560	−	0.817759i	$-0.695216\pi$
$617$	−28.5932	−1.15112	−0.575560	+	0.817759i	$0.695216\pi$
$618$	−0.604394	−0.0243123
$619$	3.01580	0.121215	0.0606076	−	0.998162i	$-0.480696\pi$
$619$	3.01580	0.121215	0.0606076	+	0.998162i	$0.480696\pi$
$620$	−9.48125	−0.380776
$621$	0	0
$622$	−66.1539	−2.65253
$623$	−5.79939	−0.232348
$624$	13.6294	0.545613
$625$	−11.8825	−0.475300
$626$	−28.3071	−1.13138
$627$	8.42702	0.336543
$628$	−37.6490	−1.50236
$629$	33.4332	1.33307
$630$	11.4676	0.456881
$631$	26.3615	1.04943	0.524717	−	0.851277i	$-0.324171\pi$
$631$	26.3615	1.04943	0.524717	+	0.851277i	$0.324171\pi$
$632$	−8.53474	−0.339494
$633$	−26.7256	−1.06225
$634$	−8.08836	−0.321230
$635$	−33.4308	−1.32666
$636$	−15.7964	−0.626369
$637$	20.4823	0.811538
$638$	29.2631	1.15854
$639$	−5.67469	−0.224487
$640$	23.6409	0.934488
$641$	−15.5390	−0.613753	−0.306877	−	0.951749i	$-0.599284\pi$
$641$	−15.5390	−0.613753	−0.306877	+	0.951749i	$0.599284\pi$
$642$	−17.4234	−0.687646
$643$	40.0898	1.58099	0.790493	−	0.612471i	$-0.209824\pi$
$643$	40.0898	1.58099	0.790493	+	0.612471i	$0.209824\pi$
$644$	0	0
$645$	−9.91596	−0.390441
$646$	−51.9254	−2.04298
$647$	−18.6564	−0.733459	−0.366730	−	0.930328i	$-0.619523\pi$
$647$	−18.6564	−0.733459	−0.366730	+	0.930328i	$0.619523\pi$
$648$	0.875613	0.0343973
$649$	−1.30704	−0.0513057
$650$	−66.0393	−2.59027
$651$	−1.79888	−0.0705037
$652$	−14.8910	−0.583177
$653$	−46.6877	−1.82703	−0.913516	−	0.406803i	$-0.866644\pi$
$653$	−46.6877	−1.82703	−0.913516	+	0.406803i	$0.866644\pi$
$654$	−43.1839	−1.68863
$655$	−39.5227	−1.54428
$656$	−14.6730	−0.572885
$657$	0.910042	0.0355041
$658$	−15.5125	−0.604740
$659$	12.3106	0.479552	0.239776	−	0.970828i	$-0.422926\pi$
$659$	12.3106	0.479552	0.239776	+	0.970828i	$0.422926\pi$
$660$	11.5031	0.447757
$661$	−35.3668	−1.37561	−0.687805	−	0.725895i	$-0.741426\pi$
$661$	−35.3668	−1.37561	−0.687805	+	0.725895i	$0.741426\pi$
$662$	−42.4699	−1.65064
$663$	−18.4215	−0.715433
$664$	4.25056	0.164954
$665$	−33.3264	−1.29234
$666$	17.3681	0.672999
$667$	0	0
$668$	22.8221	0.883014
$669$	12.2946	0.475338
$670$	−20.2484	−0.782263
$671$	1.05193	0.0406094
$672$	12.7197	0.490672
$673$	−0.700020	−0.0269838	−0.0134919	−	0.999909i	$-0.504295\pi$
$673$	−0.700020	−0.0269838	−0.0134919	+	0.999909i	$0.504295\pi$
$674$	−23.1432	−0.891443
$675$	6.90085	0.265614
$676$	18.6930	0.718963
$677$	11.4154	0.438730	0.219365	−	0.975643i	$-0.429601\pi$
$677$	11.4154	0.438730	0.219365	+	0.975643i	$0.429601\pi$
$678$	3.41047	0.130978
$679$	−2.69862	−0.103563
$680$	−12.2201	−0.468618
$681$	16.4827	0.631619
$682$	−3.29779	−0.126279
$683$	24.6583	0.943524	0.471762	−	0.881726i	$-0.343618\pi$
$683$	24.6583	0.943524	0.471762	+	0.881726i	$0.343618\pi$
$684$	−14.7596	−0.564346
$685$	5.67045	0.216657
$686$	38.2216	1.45931
$687$	0.636413	0.0242807
$688$	−8.60339	−0.328001
$689$	29.7646	1.13394
$690$	0	0
$691$	16.2668	0.618819	0.309410	−	0.950929i	$-0.399869\pi$
$691$	16.2668	0.618819	0.309410	+	0.950929i	$0.399869\pi$
$692$	17.1435	0.651698
$693$	2.18249	0.0829058
$694$	−55.4038	−2.10310
$695$	19.2360	0.729661
$696$	−8.83635	−0.334941
$697$	19.8321	0.751194
$698$	39.2917	1.48721
$699$	0.643582	0.0243425
$700$	−26.3787	−0.997023
$701$	−24.2283	−0.915090	−0.457545	−	0.889186i	$-0.651271\pi$
$701$	−24.2283	−0.915090	−0.457545	+	0.889186i	$0.651271\pi$
$702$	−9.56973	−0.361186
$703$	−50.4738	−1.90366
$704$	15.0585	0.567540
$705$	−16.0985	−0.606306
$706$	49.5714	1.86564
$707$	−10.8909	−0.409594
$708$	2.28922	0.0860342
$709$	20.3858	0.765604	0.382802	−	0.923830i	$-0.374959\pi$
$709$	20.3858	0.765604	0.382802	+	0.923830i	$0.374959\pi$
$710$	41.1413	1.54400
$711$	−9.74717	−0.365547
$712$	3.21038	0.120314
$713$	0	0
$714$	−13.4480	−0.503278
$715$	−21.6748	−0.810591
$716$	19.3981	0.724943
$717$	−9.62895	−0.359600
$718$	31.6402	1.18080
$719$	−23.4769	−0.875540	−0.437770	−	0.899087i	$-0.644232\pi$
$719$	−23.4769	−0.875540	−0.437770	+	0.899087i	$0.644232\pi$
$720$	10.3255	0.384810
$721$	0.454896	0.0169412
$722$	38.4613	1.43138
$723$	5.96496	0.221839
$724$	28.4900	1.05882
$725$	−69.6408	−2.58639
$726$	−19.1164	−0.709475
$727$	−21.6990	−0.804771	−0.402385	−	0.915470i	$-0.631819\pi$
$727$	−21.6990	−0.804771	−0.402385	+	0.915470i	$0.631819\pi$
$728$	6.30672	0.233743
$729$	1.00000	0.0370370
$730$	−6.59777	−0.244194
$731$	11.6284	0.430090
$732$	−1.84242	−0.0680977
$733$	−32.3971	−1.19661	−0.598307	−	0.801267i	$-0.704160\pi$
$733$	−32.3971	−1.19661	−0.598307	+	0.801267i	$0.704160\pi$
$734$	−69.6682	−2.57150
$735$	15.5172	0.572362
$736$	0	0
$737$	−3.85361	−0.141949
$738$	10.3025	0.379240
$739$	36.5732	1.34537	0.672683	−	0.739931i	$-0.265142\pi$
$739$	36.5732	1.34537	0.672683	+	0.739931i	$0.265142\pi$
$740$	−68.8981	−2.53274
$741$	27.8109	1.02166
$742$	21.7286	0.797681
$743$	−27.8032	−1.02000	−0.510001	−	0.860174i	$-0.670355\pi$
$743$	−27.8032	−1.02000	−0.510001	+	0.860174i	$0.670355\pi$
$744$	0.995808	0.0365081
$745$	20.9811	0.768687
$746$	−69.2218	−2.53439
$747$	4.85439	0.177613
$748$	−13.4896	−0.493228
$749$	13.1137	0.479164
$750$	−13.7811	−0.503214
$751$	24.5221	0.894824	0.447412	−	0.894328i	$-0.352346\pi$
$751$	24.5221	0.894824	0.447412	+	0.894328i	$0.352346\pi$
$752$	−13.9676	−0.509345
$753$	3.85471	0.140473
$754$	96.5740	3.51702
$755$	81.6464	2.97142
$756$	−3.82253	−0.139024
$757$	49.9792	1.81652	0.908262	−	0.418402i	$-0.137410\pi$
$757$	49.9792	1.81652	0.908262	+	0.418402i	$0.137410\pi$
$758$	−46.2460	−1.67973
$759$	0	0
$760$	18.4485	0.669199
$761$	−0.903993	−0.0327697	−0.0163849	−	0.999866i	$-0.505216\pi$
$761$	−0.903993	−0.0327697	−0.0163849	+	0.999866i	$0.505216\pi$
$762$	20.3659	0.737780
$763$	32.5023	1.17666
$764$	63.9196	2.31253
$765$	−13.9560	−0.504581
$766$	−9.84070	−0.355559
$767$	−4.31349	−0.155751
$768$	7.42536	0.267940
$769$	−46.9777	−1.69406	−0.847030	−	0.531546i	$-0.821611\pi$
$769$	−46.9777	−1.69406	−0.847030	+	0.531546i	$0.821611\pi$
$770$	−15.8229	−0.570218
$771$	−11.8109	−0.425358
$772$	45.5512	1.63942
$773$	−42.2237	−1.51868	−0.759340	−	0.650694i	$-0.774478\pi$
$773$	−42.2237	−1.51868	−0.759340	+	0.650694i	$0.774478\pi$
$774$	6.04077	0.217131
$775$	7.84813	0.281913
$776$	1.49388	0.0536270
$777$	−13.0721	−0.468957
$778$	29.4862	1.05713
$779$	−29.9403	−1.07272
$780$	37.9625	1.35928
$781$	7.82988	0.280175
$782$	0	0
$783$	−10.0916	−0.360645
$784$	13.4632	0.480829
$785$	53.7440	1.91820
$786$	24.0771	0.858801
$787$	−18.7438	−0.668144	−0.334072	−	0.942548i	$-0.608423\pi$
$787$	−18.7438	−0.668144	−0.334072	+	0.942548i	$0.608423\pi$
$788$	21.3104	0.759151
$789$	−14.6534	−0.521676
$790$	70.6665	2.51420
$791$	−2.56689	−0.0912680
$792$	−1.20816	−0.0429301
$793$	3.47159	0.123280
$794$	23.6666	0.839896
$795$	22.5494	0.799745
$796$	−36.2643	−1.28536
$797$	48.2282	1.70833	0.854165	−	0.520002i	$-0.174069\pi$
$797$	48.2282	1.70833	0.854165	+	0.520002i	$0.174069\pi$
$798$	20.3023	0.718695
$799$	18.8786	0.667877
$800$	−55.4932	−1.96198
$801$	3.66643	0.129547
$802$	35.9860	1.27071
$803$	−1.25567	−0.0443115
$804$	6.74944	0.238034
$805$	0	0
$806$	−10.8834	−0.383350
$807$	−27.2170	−0.958083
$808$	6.02889	0.212096
$809$	−53.2038	−1.87055	−0.935273	−	0.353928i	$-0.884846\pi$
$809$	−53.2038	−1.87055	−0.935273	+	0.353928i	$0.884846\pi$
$810$	−7.24995	−0.254737
$811$	3.68024	0.129231	0.0646153	−	0.997910i	$-0.479418\pi$
$811$	3.68024	0.129231	0.0646153	+	0.997910i	$0.479418\pi$
$812$	38.5756	1.35374
$813$	−4.28396	−0.150245
$814$	−23.9643	−0.839947
$815$	21.2569	0.744597
$816$	−12.1087	−0.423888
$817$	−17.5552	−0.614180
$818$	−18.8757	−0.659973
$819$	7.20264	0.251681
$820$	−40.8693	−1.42722
$821$	2.44781	0.0854291	0.0427146	−	0.999087i	$-0.486399\pi$
$821$	2.44781	0.0854291	0.0427146	+	0.999087i	$0.486399\pi$
$822$	−3.45442	−0.120487
$823$	0.887969	0.0309527	0.0154763	−	0.999880i	$-0.495074\pi$
$823$	0.887969	0.0309527	0.0154763	+	0.999880i	$0.495074\pi$
$824$	−0.251818	−0.00877248
$825$	−9.52172	−0.331504
$826$	−3.14891	−0.109564
$827$	−25.9780	−0.903343	−0.451671	−	0.892184i	$-0.649172\pi$
$827$	−25.9780	−0.903343	−0.451671	+	0.892184i	$0.649172\pi$
$828$	0	0
$829$	−18.5613	−0.644662	−0.322331	−	0.946627i	$-0.604466\pi$
$829$	−18.5613	−0.644662	−0.322331	+	0.946627i	$0.604466\pi$
$830$	−35.1941	−1.22160
$831$	6.86176	0.238032
$832$	49.6962	1.72291
$833$	−18.1969	−0.630486
$834$	−11.7185	−0.405778
$835$	−32.5786	−1.12743
$836$	20.3651	0.704342
$837$	1.13727	0.0393098
$838$	14.7991	0.511228
$839$	17.0133	0.587366	0.293683	−	0.955903i	$-0.405119\pi$
$839$	17.0133	0.587366	0.293683	+	0.955903i	$0.405119\pi$
$840$	4.77793	0.164854
$841$	72.8408	2.51175
$842$	−25.8437	−0.890633
$843$	13.3058	0.458275
$844$	−64.5863	−2.22315
$845$	−26.6843	−0.917968
$846$	9.80716	0.337177
$847$	14.3879	0.494374
$848$	19.5646	0.671850
$849$	−19.2217	−0.659689
$850$	58.6707	2.01239
$851$	0	0
$852$	−13.7137	−0.469824
$853$	33.0854	1.13282	0.566411	−	0.824123i	$-0.308331\pi$
$853$	33.0854	1.13282	0.566411	+	0.824123i	$0.308331\pi$
$854$	2.53431	0.0867223
$855$	21.0693	0.720555
$856$	−7.25936	−0.248120
$857$	−10.0151	−0.342110	−0.171055	−	0.985262i	$-0.554718\pi$
$857$	−10.0151	−0.342110	−0.171055	+	0.985262i	$0.554718\pi$
$858$	13.2042	0.450784
$859$	37.7898	1.28937	0.644686	−	0.764447i	$-0.276988\pi$
$859$	37.7898	1.28937	0.644686	+	0.764447i	$0.276988\pi$
$860$	−23.9634	−0.817143
$861$	−7.75415	−0.264261
$862$	−10.5985	−0.360986
$863$	38.7898	1.32042	0.660210	−	0.751081i	$-0.270467\pi$
$863$	38.7898	1.32042	0.660210	+	0.751081i	$0.270467\pi$
$864$	−8.04151	−0.273578
$865$	−24.4724	−0.832085
$866$	1.86945	0.0635266
$867$	−0.633899	−0.0215283
$868$	−4.34726	−0.147555
$869$	13.4490	0.456227
$870$	73.1638	2.48048
$871$	−12.7177	−0.430922
$872$	−17.9924	−0.609298
$873$	1.70609	0.0577425
$874$	0	0
$875$	10.3723	0.350648
$876$	2.19925	0.0743057
$877$	−23.7055	−0.800477	−0.400238	−	0.916411i	$-0.631073\pi$
$877$	−23.7055	−0.800477	−0.400238	+	0.916411i	$0.631073\pi$
$878$	83.8188	2.82875
$879$	−13.6447	−0.460225
$880$	−14.2471	−0.480269
$881$	−19.7637	−0.665857	−0.332929	−	0.942952i	$-0.608037\pi$
$881$	−19.7637	−0.665857	−0.332929	+	0.942952i	$0.608037\pi$
$882$	−9.45304	−0.318300
$883$	26.5396	0.893130	0.446565	−	0.894751i	$-0.352647\pi$
$883$	26.5396	0.893130	0.446565	+	0.894751i	$0.352647\pi$
$884$	−44.5183	−1.49731
$885$	−3.26786	−0.109848
$886$	26.9219	0.904459
$887$	−12.8547	−0.431620	−0.215810	−	0.976435i	$-0.569239\pi$
$887$	−12.8547	−0.431620	−0.215810	+	0.976435i	$0.569239\pi$
$888$	7.23631	0.242835
$889$	−15.3284	−0.514098
$890$	−26.5815	−0.891013
$891$	−1.37979	−0.0462247
$892$	29.7118	0.994824
$893$	−28.5009	−0.953745
$894$	−12.7816	−0.427480
$895$	−27.6909	−0.925604
$896$	10.8396	0.362125
$897$	0	0
$898$	−28.0436	−0.935827
$899$	−11.4769	−0.382776
$900$	16.6769	0.555897
$901$	−26.4435	−0.880961
$902$	−14.2153	−0.473316
$903$	−4.54657	−0.151301
$904$	1.42096	0.0472603
$905$	−40.6695	−1.35190
$906$	−49.7387	−1.65246
$907$	40.0575	1.33009	0.665044	−	0.746804i	$-0.268413\pi$
$907$	40.0575	1.33009	0.665044	+	0.746804i	$0.268413\pi$
$908$	39.8329	1.32190
$909$	6.88534	0.228372
$910$	−52.2188	−1.73104
$911$	45.6764	1.51333	0.756663	−	0.653806i	$-0.226829\pi$
$911$	45.6764	1.51333	0.756663	+	0.653806i	$0.226829\pi$
$912$	18.2804	0.605323
$913$	−6.69803	−0.221672
$914$	−48.4677	−1.60317
$915$	2.63005	0.0869468
$916$	1.53799	0.0508165
$917$	−18.1216	−0.598427
$918$	8.50196	0.280606
$919$	−9.12733	−0.301083	−0.150541	−	0.988604i	$-0.548102\pi$
$919$	−9.12733	−0.301083	−0.150541	+	0.988604i	$0.548102\pi$
$920$	0	0
$921$	−25.4313	−0.837991
$922$	−15.9717	−0.526000
$923$	25.8402	0.850540
$924$	5.27429	0.173511
$925$	57.0306	1.87515
$926$	21.3677	0.702187
$927$	−0.287590	−0.00944570
$928$	81.1518	2.66394
$929$	0.583776	0.0191531	0.00957653	−	0.999954i	$-0.496952\pi$
$929$	0.583776	0.0191531	0.00957653	+	0.999954i	$0.496952\pi$
$930$	−8.24516	−0.270369
$931$	27.4717	0.900350
$932$	1.55531	0.0509458
$933$	−31.4782	−1.03055
$934$	21.7156	0.710557
$935$	19.2564	0.629751
$936$	−3.98717	−0.130325
$937$	52.5112	1.71547	0.857733	−	0.514096i	$-0.171873\pi$
$937$	52.5112	1.71547	0.857733	+	0.514096i	$0.171873\pi$
$938$	−9.28410	−0.303136
$939$	−13.4694	−0.439559
$940$	−38.9044	−1.26892
$941$	53.3424	1.73891	0.869456	−	0.494010i	$-0.164469\pi$
$941$	53.3424	1.73891	0.869456	+	0.494010i	$0.164469\pi$
$942$	−32.7406	−1.06675
$943$	0	0
$944$	−2.83530	−0.0922811
$945$	5.45667	0.177505
$946$	−8.33498	−0.270994
$947$	−12.7808	−0.415319	−0.207659	−	0.978201i	$-0.566585\pi$
$947$	−12.7808	−0.415319	−0.207659	+	0.978201i	$0.566585\pi$
$948$	−23.5554	−0.765045
$949$	−4.14395	−0.134518
$950$	−88.5748	−2.87374
$951$	−3.84870	−0.124803
$952$	−5.60303	−0.181595
$953$	26.8697	0.870394	0.435197	−	0.900335i	$-0.356679\pi$
$953$	26.8697	0.870394	0.435197	+	0.900335i	$0.356679\pi$
$954$	−13.7370	−0.444752
$955$	−91.2453	−2.95263
$956$	−23.2697	−0.752597
$957$	13.9243	0.450109
$958$	18.3076	0.591491
$959$	2.59996	0.0839571
$960$	37.6495	1.21513
$961$	−29.7066	−0.958278
$962$	−79.0869	−2.54987
$963$	−8.29060	−0.267161
$964$	14.4152	0.464282
$965$	−65.0244	−2.09321
$966$	0	0
$967$	12.5704	0.404236	0.202118	−	0.979361i	$-0.435218\pi$
$967$	12.5704	0.404236	0.202118	+	0.979361i	$0.435218\pi$
$968$	−7.96473	−0.255996
$969$	−24.7078	−0.793728
$970$	−12.3691	−0.397148
$971$	19.9924	0.641585	0.320793	−	0.947149i	$-0.396051\pi$
$971$	19.9924	0.641585	0.320793	+	0.947149i	$0.396051\pi$
$972$	2.41664	0.0775139
$973$	8.81989	0.282753
$974$	47.8475	1.53313
$975$	−31.4236	−1.00636
$976$	2.28191	0.0730422
$977$	27.6322	0.884031	0.442015	−	0.897007i	$-0.354264\pi$
$977$	27.6322	0.884031	0.442015	+	0.897007i	$0.354264\pi$
$978$	−12.9496	−0.414084
$979$	−5.05891	−0.161683
$980$	37.4996	1.19788
$981$	−20.5483	−0.656057
$982$	58.9350	1.88069
$983$	−23.5308	−0.750515	−0.375258	−	0.926921i	$-0.622446\pi$
$983$	−23.5308	−0.750515	−0.375258	+	0.926921i	$0.622446\pi$
$984$	4.29247	0.136839
$985$	−30.4206	−0.969280
$986$	−85.7985	−2.73238
$987$	−7.38135	−0.234951
$988$	67.2089	2.13820
$989$	0	0
$990$	10.0034	0.317929
$991$	42.8907	1.36247	0.681234	−	0.732066i	$-0.261444\pi$
$991$	42.8907	1.36247	0.681234	+	0.732066i	$0.261444\pi$
$992$	−9.14537	−0.290366
$993$	−20.2085	−0.641298
$994$	18.8637	0.598321
$995$	51.7674	1.64114
$996$	11.7313	0.371721
$997$	−38.8923	−1.23173	−0.615866	−	0.787851i	$-0.711194\pi$
$997$	−38.8923	−1.23173	−0.615866	+	0.787851i	$0.711194\pi$
$998$	−30.7857	−0.974503
$999$	8.26429	0.261470

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1587.2.a.t.1.10		10
3.2	odd	2		4761.2.a.bu.1.1		10
23.17	odd	22		69.2.e.c.13.1	✓	20
23.19	odd	22		69.2.e.c.16.1	yes	20
23.22	odd	2		1587.2.a.u.1.10		10
69.17	even	22		207.2.i.d.82.2		20
69.65	even	22		207.2.i.d.154.2		20
69.68	even	2		4761.2.a.bt.1.1		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
69.2.e.c.13.1	✓	20	23.17	odd	22
69.2.e.c.16.1	yes	20	23.19	odd	22
207.2.i.d.82.2		20	69.17	even	22
207.2.i.d.154.2		20	69.65	even	22
1587.2.a.t.1.10		10	1.1	even	1	trivial
1587.2.a.u.1.10		10	23.22	odd	2
4761.2.a.bt.1.1		10	69.68	even	2
4761.2.a.bu.1.1		10	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1587 = 3 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1587.a (trivial)

\(f(q)\)	\(=\)	\(q+2.10158 q^{2} +1.00000 q^{3} +2.41664 q^{4} -3.44976 q^{5} +2.10158 q^{6} -1.58175 q^{7} +0.875613 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+2.10158 q^{2} +1.00000 q^{3} +2.41664 q^{4} -3.44976 q^{5} +2.10158 q^{6} -1.58175 q^{7} +0.875613 q^{8} +1.00000 q^{9} -7.24995 q^{10} -1.37979 q^{11} +2.41664 q^{12} -4.55358 q^{13} -3.32418 q^{14} -3.44976 q^{15} -2.99312 q^{16} +4.04550 q^{17} +2.10158 q^{18} -6.10747 q^{19} -8.33685 q^{20} -1.58175 q^{21} -2.89974 q^{22} +0.875613 q^{24} +6.90085 q^{25} -9.56973 q^{26} +1.00000 q^{27} -3.82253 q^{28} -10.0916 q^{29} -7.24995 q^{30} +1.13727 q^{31} -8.04151 q^{32} -1.37979 q^{33} +8.50196 q^{34} +5.45667 q^{35} +2.41664 q^{36} +8.26429 q^{37} -12.8353 q^{38} -4.55358 q^{39} -3.02065 q^{40} +4.90225 q^{41} -3.32418 q^{42} +2.87439 q^{43} -3.33446 q^{44} -3.44976 q^{45} +4.66656 q^{47} -2.99312 q^{48} -4.49806 q^{49} +14.5027 q^{50} +4.04550 q^{51} -11.0044 q^{52} -6.53652 q^{53} +2.10158 q^{54} +4.75994 q^{55} -1.38500 q^{56} -6.10747 q^{57} -21.2084 q^{58} +0.947273 q^{59} -8.33685 q^{60} -0.762386 q^{61} +2.39007 q^{62} -1.58175 q^{63} -10.9136 q^{64} +15.7088 q^{65} -2.89974 q^{66} +2.79290 q^{67} +9.77655 q^{68} +11.4676 q^{70} -5.67469 q^{71} +0.875613 q^{72} +0.910042 q^{73} +17.3681 q^{74} +6.90085 q^{75} -14.7596 q^{76} +2.18249 q^{77} -9.56973 q^{78} -9.74717 q^{79} +10.3255 q^{80} +1.00000 q^{81} +10.3025 q^{82} +4.85439 q^{83} -3.82253 q^{84} -13.9560 q^{85} +6.04077 q^{86} -10.0916 q^{87} -1.20816 q^{88} +3.66643 q^{89} -7.24995 q^{90} +7.20264 q^{91} +1.13727 q^{93} +9.80716 q^{94} +21.0693 q^{95} -8.04151 q^{96} +1.70609 q^{97} -9.45304 q^{98} -1.37979 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 2 q^{2} + 10 q^{3} + 8 q^{4} - 8 q^{5} - 2 q^{6} - 19 q^{7} - 6 q^{8} + 10 q^{9}+O(q^{10}) \) 10 * q - 2 * q^2 + 10 * q^3 + 8 * q^4 - 8 * q^5 - 2 * q^6 - 19 * q^7 - 6 * q^8 + 10 * q^9	\( 10 q - 2 q^{2} + 10 q^{3} + 8 q^{4} - 8 q^{5} - 2 q^{6} - 19 q^{7} - 6 q^{8} + 10 q^{9} - 13 q^{10} - 3 q^{11} + 8 q^{12} - 4 q^{13} - 8 q^{15} - 4 q^{16} - 11 q^{17} - 2 q^{18} - 22 q^{19} - q^{20} - 19 q^{21} - 13 q^{22} - 6 q^{24} - 2 q^{25} + 4 q^{26} + 10 q^{27} - 26 q^{28} - 5 q^{29} - 13 q^{30} - 7 q^{31} - 34 q^{32} - 3 q^{33} - 4 q^{34} + 9 q^{35} + 8 q^{36} - 35 q^{37} + 9 q^{38} - 4 q^{39} - 21 q^{40} - 28 q^{43} + 7 q^{44} - 8 q^{45} + 9 q^{47} - 4 q^{48} + 17 q^{49} - 11 q^{51} - 52 q^{52} - 34 q^{53} - 2 q^{54} - 14 q^{55} + 30 q^{56} - 22 q^{57} - 24 q^{58} - 2 q^{59} - q^{60} - 49 q^{61} - 28 q^{62} - 19 q^{63} + 10 q^{64} - 2 q^{65} - 13 q^{66} - 26 q^{67} + 6 q^{68} + 16 q^{70} + 15 q^{71} - 6 q^{72} + 14 q^{73} + 25 q^{74} - 2 q^{75} - 19 q^{76} - 33 q^{77} + 4 q^{78} - 43 q^{79} + 49 q^{80} + 10 q^{81} + 24 q^{82} + 15 q^{83} - 26 q^{84} - 21 q^{85} + 49 q^{86} - 5 q^{87} - 15 q^{88} + 15 q^{89} - 13 q^{90} - 4 q^{91} - 7 q^{93} - 28 q^{94} + 28 q^{95} - 34 q^{96} - 22 q^{97} + 15 q^{98} - 3 q^{99}+O(q^{100}) \) 10 * q - 2 * q^2 + 10 * q^3 + 8 * q^4 - 8 * q^5 - 2 * q^6 - 19 * q^7 - 6 * q^8 + 10 * q^9 - 13 * q^10 - 3 * q^11 + 8 * q^12 - 4 * q^13 - 8 * q^15 - 4 * q^16 - 11 * q^17 - 2 * q^18 - 22 * q^19 - q^20 - 19 * q^21 - 13 * q^22 - 6 * q^24 - 2 * q^25 + 4 * q^26 + 10 * q^27 - 26 * q^28 - 5 * q^29 - 13 * q^30 - 7 * q^31 - 34 * q^32 - 3 * q^33 - 4 * q^34 + 9 * q^35 + 8 * q^36 - 35 * q^37 + 9 * q^38 - 4 * q^39 - 21 * q^40 - 28 * q^43 + 7 * q^44 - 8 * q^45 + 9 * q^47 - 4 * q^48 + 17 * q^49 - 11 * q^51 - 52 * q^52 - 34 * q^53 - 2 * q^54 - 14 * q^55 + 30 * q^56 - 22 * q^57 - 24 * q^58 - 2 * q^59 - q^60 - 49 * q^61 - 28 * q^62 - 19 * q^63 + 10 * q^64 - 2 * q^65 - 13 * q^66 - 26 * q^67 + 6 * q^68 + 16 * q^70 + 15 * q^71 - 6 * q^72 + 14 * q^73 + 25 * q^74 - 2 * q^75 - 19 * q^76 - 33 * q^77 + 4 * q^78 - 43 * q^79 + 49 * q^80 + 10 * q^81 + 24 * q^82 + 15 * q^83 - 26 * q^84 - 21 * q^85 + 49 * q^86 - 5 * q^87 - 15 * q^88 + 15 * q^89 - 13 * q^90 - 4 * q^91 - 7 * q^93 - 28 * q^94 + 28 * q^95 - 34 * q^96 - 22 * q^97 + 15 * q^98 - 3 * q^99

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